Question

If a hydrogen atom at rest, emits a photon of wavelength $\lambda ,$ the recoil speed of the atom of mass ${}^{\prime }{m}^{\prime }$ is given by

• A. $\frac{h}{m\lambda }$
• B. $\frac{mh}{\lambda }$
• C. $mh\lambda$
• D. none of these

Answer 1

The correct option is A $\frac{h}{m\lambda }$

From conservation of momentum,
$P=const={\overrightarrow{p}}_{photon}+{\overrightarrow{p}}_{atom}=0$
Now, from de-broglie:
$\lambda =\frac{h}{mv}\Rightarrow v=\frac{h}{m\lambda }$

So, the answer is option (A).